Brazilian pepper tree

Our neighbor has a Brazilian pepper tree (the trunk is just on their side of the wooden fence). This full-grown tree drops red berries all over our deck. We offered to pay for the tree to be cut down and something else planted there. The neighbor objected, but we have learned that the Brazilian Pepper tree is a nightmare to deal with. We have cut the branches that go over our side (at a cost of $2,300), but is there anything else we can do about this problem because we are still having to vacuum berries so they don't grow on our side.
Thanks, Dave